From atomistic systems to linearized continuum models for elastic materials with voids

TL;DR

This paper rigorously derives linearized continuum models for elastic solids with voids from atomistic models, using discrete-to-continuum analysis and geometric rigidity results, advancing understanding of material behavior at multiple scales.

Contribution

It introduces a novel discrete-to-continuum analysis framework for modeling void formation in elastic materials, incorporating curvature regularization at the discrete level.

Findings

Effective continuum models are derived for materials with voids.

The analysis employs recent geometric rigidity results in variable domains.

The approach bridges atomistic and continuum descriptions of elastic materials.

Abstract

We study an atomistic model that describes the microscopic formation of material voids inside elastically stressed solids under an additional curvature regularization at the discrete level. Using a discrete-to-continuum analysis, by means of a recent geometric rigidity result in variable domains [27] and {\Gamma}-convergence tools, we rigorously derive effective linearized continuum models for elastically stressed solids with material voids in three-dimensional elasticity.